Problem: Simplify the following expression: $a = \dfrac{q^2 + 14q + 48}{q + 8} $
Answer: First factor the polynomial in the numerator. $ q^2 + 14q + 48 = (q + 8)(q + 6) $ So we can rewrite the expression as: $a = \dfrac{(q + 8)(q + 6)}{q + 8} $ We can divide the numerator and denominator by $(q + 8)$ on condition that $q \neq -8$ Therefore $a = q + 6; q \neq -8$